Can we use a neural network that is trained using Reinforcement Learning for dynamic game level difficulty designing in realtime?
There have been many researches in dynamic difficulty adjustment (DDA). I see this one is quite explaining: AI for Dynamic Difficulty Adjustment in Games. However, there are many factors when we are trying to do dynamic difficulty adjustment. As explained in paper above, one major problem is it is sometimes hard to make sure the created model will still deliver the intended experience.

You can also read this paper about game design and DDA on ace05The Case for Dynamic Difficulty Adjustment in Games .

So for short, you can use neural network -- or other learning methods -- to do dynamic difficulty adjustment. But it's more about game design and experience impact of your DDA.